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VARVARA [1.3K]
3 years ago
13

What is the shape of the cross-section formed when a plane containing line AC and line EH intersects this cube? What is the area

of the cross-section? In two or more complete sentences, explain how you were able to determine the shape and area of the cross-section. Be sure to include the properties of quadrilaterals and the mathematical computations necessary to support your answers

Mathematics
1 answer:
velikii [3]3 years ago
4 0

Answer:

Cross section is a rectangle.

Area of cross section = 16 sqrt(2) = 22.63 sq. units (to 2 decimals)

Step-by-step explanation:

Given a cube.

top face ABCD is parallel and congruent to bottom face EFGH  ........(1)

justified by the properties of cubes

Sides AE and CH are perpendicular to faces ABCD and EFGH ..........(2)

justified by the properties of cubes

Diagonals AC and EH are congruent ......................(3)

justified by (1), congruent top and bottom faces  

Consider cross-section ACHE

AC is congruent and parallel to  EH   (1) & (3)

EA & HC are perpendicular to AC      (2)

Therefore the quadrilateral ACHE is a rectangle.

Length of diagonal AC = sqrt(4^2+4^2) = 4 sqrt(2)  ..........pythagoras theorem

AE = CH = DG = 4      properties of cube, all sides equal

Area of ACHE = 4* 4sqrt(2) = 16 sqrt(2) = 22.63 sq. units

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find the value of x if A, B and C are collinear points and B is between A and C. AB= 6x, BC= x-5, AC= 23
Irina18 [472]

Answer:

x=4

Step-by-step explanation:

AB + BC = AC

AB= 6x, BC= x-5, AC= 23

Substituting what we know

6x + x-5 = 23

Combine like terms

7x -5 = 23

Add 5 to each side

7x-5+5 =23+5

7x = 28

Divide each side by 7

7x/7 = 28/7

x=4

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3 years ago
Rusty's hair grows at the rate of 1 over 4 inch per month.
Nadya [2.5K]
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8 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=4x%20%7B%7D%5E%7B2%7D%20%20%2B%2020x%20%2B%2025" id="TexFormula1" title="4x {}^{2} + 20x + 25
BigorU [14]

\sf{\qquad\qquad\huge\underline{{\sf Answer}}}

Let's Solve ~

\qquad \sf  \dashrightarrow \: 4 {x}^{2}  + 20x + 25

\qquad \sf  \dashrightarrow \: 4 {x}^{2}  + 10x + 10x + 25

\qquad \sf  \dashrightarrow \: 2x(2x + 5) + 5(2x + 5)

\qquad \sf  \dashrightarrow \: (2x + 5) (2x + 5)

\qquad \sf  \dashrightarrow \: (2x + 5) {}^{2}

or

\sf{\qquad \sf  \dashrightarrow \: 4x² + 20x + 25 }

\sf{\qquad \sf  \dashrightarrow \: (2x)² + (2 \sdot 2x \sdot 5) + (5)²}

[ it's similar to expression - a² + 2ab + b² that is equal to (a + b)² ]

so, let's use this identity here to factorise :

\sf{\qquad \sf  \dashrightarrow \: (2x + 5)²}

I hope it was helpful ~

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2 years ago
F(x)=|x+3|-1 range and domain
KiRa [710]

Hey there! :)

Answer:

Domain: (-∞, ∞)

Range: [-1, ∞)

Step-by-step explanation:

This is an absolute-value function.  (Graphed below) The vertex is at (-3, -1) which consists of the minimum y-value of the function. Therefore:

Domain: (-∞, ∞)

Range: [-1, ∞)

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3 years ago
OH GOD PLEASE HELP ME MY BRAIN HURTS!
alukav5142 [94]
Your answer should be 71. :)
8 0
3 years ago
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